{"paper":{"title":"Periodic orbits for an infinite family of classical superintegrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","nlin.SI","physics.class-ph","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V. Turbiner, Fr\\'ed\\'erick Tremblay, Pavel Winternitz","submitted_at":"2009-10-02T00:43:11Z","abstract_excerpt":"We show that all bounded trajectories in the two dimensional classical system with the potential $V(r,\\phi)=\\omega^2 r^2+ \\frac{\\al k^2}{r^2 \\cos^2 {k \\phi}}+ \\frac{\\beta k^2}{r^2 \\sin^2 {k \\phi}}$ are closed for all integer and rational values of $k$. The period is $T=\\frac{\\pi}{2\\omega}$ and does not depend on $k$. This agrees with our earlier conjecture suggesting that the quantum version of this system is superintegrable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0299","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}